Free vibration of ferromagnetic functionally graded cylindrical shells subjected to magnetic and temperature fields

The free vibration characteristics of functionally graded cylindrical shells under magnetic and temperature fields are investigated. According to Donnell's theory, the kinetic energy, deformation energy, and their variational expressions are obtained. Based on the electromagnetic elasticity theory, the eddy current electromagnetic and magnetization force models are established. Using Hamilton's principle, the magneto-thermo-elastic free vibration partial differential equations are derived. The modal frequency differential matrix equation with diverse boundary conditions is derived from the Galerkin integral technique. Through numerical examples, the curves and three-dimensional surface diagrams depicting the variations for the natural frequency with diverse parameters are obtained. The feasibility of the proposed solution method in this paper is supported by literature examples. The influence of magnetic induction intensity, temperature, power-law index, wave number, and shell dimension on the natural frequencies are determined.